Bangs Leisure Chairs produces three types of handcrafted outdoor chairs that are popular for beach, pool, and patios: sling chairs, Adirondack chairs, and hammocks. The unit profit for these products is $$40,$ $$100,$ and $$90,$ respectively. Each type of chair requires cutting, assembling, and finishing. The owner is retired and is willing to work six hours$/$day for five days$/$week$,$ so has $120$ hours available each month. He does not want to spend more than $50$ hours each month on any one activity $($that is$,$ cutting, assembling, and finishing$).$ The retailer he works with is certain that all products he makes can easily be sold. Sling chairs are made up of ten wood pieces for the frame and one piece of cloth. The actual cutting of the wood takes $30$ minutes. Assembling includes sewing of the fabric and the attachment of rivets, screws, fabric, and dowel rods, and takes $45$ minutes. The finishing stage involves sanding, staining, and varnishing of the various parts and takes one hour. Adirondack chairs take two hours for both the cutting and assembling phases, and finishing takes one hour. For hammocks, cutting takes $0\mathrm{.}4$ hour; assembly takes three hours; and finishing also takes one hour. How many of each type of chair should he produce each month to maximize profit? What is the maximum amount of time you can spend on the assembly task in any given month.What is the maximum profit when you solve this as a linear optimization problem.Suppose that Mr$.$ Bangs wants to limit the number of Adirondack chairs to at most $20.$ Modify and re$-$solve your model to determine the new optimal solution Suppose that Mr$.$ Bangs does not want to spend more than $40$ hours each month on any one activity. Modify and re$-$solve your original model to determine the new solution.